Space of modular forms of level 736 and weight 2

• Label: 736.2
• Level: 736
• Weight: 2
• Dimension: 9258
• Nonzero newspaces: 12
• Newform subspaces: 32
• Sturm bound: 67584
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(67584\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(736))\).

	Total	New	Old
Modular forms	17600	9678	7922
Cusp forms	16193	9258	6935
Eisenstein series	1407	420	987

Trace form

9258 * q - 80 * q^2 - 58 * q^3 - 80 * q^4 - 76 * q^5 - 80 * q^6 - 58 * q^7 - 80 * q^8 - 118 * q^9 - 96 * q^10 - 58 * q^11 - 112 * q^12 - 92 * q^13 - 112 * q^14 - 66 * q^15 - 120 * q^16 - 48 * q^17 - 120 * q^18 - 58 * q^19 - 112 * q^20 - 80 * q^21 - 104 * q^22 - 70 * q^23 - 144 * q^24 - 122 * q^25 - 40 * q^26 - 106 * q^27 - 40 * q^28 - 60 * q^29 - 16 * q^30 - 98 * q^31 - 40 * q^32 - 204 * q^33 - 56 * q^34 - 106 * q^35 - 24 * q^36 - 76 * q^37 - 96 * q^38 - 106 * q^39 - 104 * q^40 - 144 * q^41 - 120 * q^42 - 74 * q^43 - 160 * q^44 - 116 * q^45 - 116 * q^46 - 132 * q^47 - 184 * q^48 - 30 * q^49 - 160 * q^50 - 50 * q^51 - 96 * q^52 - 140 * q^53 - 104 * q^54 + 6 * q^55 - 104 * q^56 - 124 * q^57 - 72 * q^58 + 6 * q^59 - 72 * q^60 - 124 * q^61 - 40 * q^62 + 30 * q^63 - 8 * q^64 - 180 * q^65 - 32 * q^66 + 22 * q^67 - 120 * q^68 - 116 * q^69 - 144 * q^70 + 6 * q^71 - 128 * q^72 - 112 * q^73 - 112 * q^74 - 34 * q^75 - 80 * q^76 - 112 * q^77 - 160 * q^78 - 66 * q^79 - 72 * q^80 - 62 * q^81 - 80 * q^82 - 138 * q^83 - 120 * q^84 - 112 * q^85 - 40 * q^86 - 170 * q^87 - 88 * q^88 - 144 * q^89 - 104 * q^90 - 176 * q^91 - 48 * q^92 - 144 * q^93 - 104 * q^94 - 178 * q^95 - 88 * q^96 - 240 * q^97 - 40 * q^98 - 162 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(736))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
736.2.a	\(\chi_{736}(1, \cdot)\)	736.2.a.a	2	1
		736.2.a.b	2
		736.2.a.c	2
		736.2.a.d	2
		736.2.a.e	3
		736.2.a.f	3
		736.2.a.g	4
		736.2.a.h	4
736.2.b	\(\chi_{736}(369, \cdot)\)	736.2.b.a	2	1
		736.2.b.b	8
		736.2.b.c	12
736.2.c	\(\chi_{736}(735, \cdot)\)	736.2.c.a	24	1
736.2.h	\(\chi_{736}(367, \cdot)\)	736.2.h.a	4	1
		736.2.h.b	6
		736.2.h.c	12
736.2.i	\(\chi_{736}(183, \cdot)\)	None	0	2
736.2.j	\(\chi_{736}(185, \cdot)\)	None	0	2
736.2.m	\(\chi_{736}(93, \cdot)\)	736.2.m.a	4	4
		736.2.m.b	164
		736.2.m.c	184
736.2.n	\(\chi_{736}(91, \cdot)\)	736.2.n.a	24	4
		736.2.n.b	352
736.2.q	\(\chi_{736}(193, \cdot)\)	736.2.q.a	10	10
		736.2.q.b	10
		736.2.q.c	20
		736.2.q.d	20
		736.2.q.e	60
		736.2.q.f	60
		736.2.q.g	60
736.2.r	\(\chi_{736}(15, \cdot)\)	736.2.r.a	220	10
736.2.w	\(\chi_{736}(63, \cdot)\)	736.2.w.a	240	10
736.2.x	\(\chi_{736}(49, \cdot)\)	736.2.x.a	220	10
736.2.ba	\(\chi_{736}(9, \cdot)\)	None	0	20
736.2.bb	\(\chi_{736}(7, \cdot)\)	None	0	20
736.2.be	\(\chi_{736}(11, \cdot)\)	736.2.be.a	3760	40
736.2.bf	\(\chi_{736}(13, \cdot)\)	736.2.bf.a	3760	40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(736))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(736)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)